Drawing a Bezier curve from two vertices
You can snap to other object's vertices just fine..

For example, just enable vertex snapping in the header, then hold &#9096; Ctrl while transforming vertices to snap:



Once you have the curve positioned, convert it to a mesh with &#9095; AltC> Mesh and join it to your mesh object by selecting both objects and pressing &#9096; CtrlJ. Note that you probably want your main mesh object to be active (last selected, with yellow outline) when you do this, so the resulting object has all the object data, modifiers, and materials that your mesh object had.